Free Work and Energy MCQs with Answers

11. Work is done on a body only when

• A. a force acts on it
• B. a force acts and the body moves with a component of displacement along the force
• C. the body is at rest
• D. the body has energy

Explanation: Work is the dot product of force and displacement, so a porter standing still holding a heavy suitcase does no work on it however tiring it feels. Carrying it horizontally also does no work against gravity, since the weight is vertical and the displacement horizontal. The joule is the work done when a force of one newton moves its point of application one metre.

12. A force of 50 N pulls a box 4 m along the floor at 60 degrees to the horizontal. The work done is

• A. 200 J
• B. 100 J
• C. 173 J
• D. 0 J

Explanation: Only the component of force along the displacement counts, so the work is 50 multiplied by 4 multiplied by cos 60, which is 200 multiplied by 0.5, giving 100 J. Ignoring the angle gives the 200 J distractor and using sin instead of cos gives 173 J. Work is a scalar, so the answer carries no direction.

13. The work done by the centripetal force on a body moving in a circle at constant speed is

• A. maximum
• B. zero
• C. equal to the kinetic energy
• D. negative

Explanation: The force points to the centre while the displacement is along the tangent, so the two are perpendicular and the dot product is zero at every instant. This is consistent with the speed and therefore the kinetic energy staying constant. A force can change the direction of motion without doing any work at all.

14. The kinetic energy of a body of mass m moving with speed v is

• A. mv
• B. half mv squared
• C. mv squared
• D. half mv

Explanation: Because the speed is squared, doubling it quadruples the kinetic energy, which is why stopping distances grow so sharply with speed. Momentum, by contrast, is mv and only doubles. The factor of one half comes from integrating the force over the distance during acceleration from rest.

15. If the speed of a car is doubled, its kinetic energy becomes

• A. double
• B. four times
• C. half
• D. unchanged

Explanation: Kinetic energy depends on the square of the speed, so a factor of two in speed gives a factor of four in energy, and the braking distance rises in the same proportion since the brakes must dissipate all of it. This is the physics behind speed limits. The momentum, meanwhile, only doubles.

16. The gravitational potential energy gained by a body of mass m raised through a height h near the Earth's surface is

• A. mgh
• B. half mgh
• C. mg divided by h
• D. mh

Explanation: The work done against a constant weight mg over a height h is mgh, and only the vertical height matters, not the path taken. Carrying a load up a ramp therefore requires the same work against gravity as lifting it straight up, though the force needed is smaller over a longer distance. Potential energy is always measured relative to a chosen zero level.

17. A body of mass 2 kg is raised 5 m. Taking g as 10 m per second squared, the potential energy gained is

• A. 10 J
• B. 50 J
• C. 100 J
• D. 25 J

Explanation: Using mgh, the energy is 2 multiplied by 10 multiplied by 5, giving 100 J. If the body were then dropped, all of it would convert to kinetic energy just before impact, giving a landing speed of 10 m per second. Forgetting to include g gives the 10 J distractor.

18. A ball is dropped from a height h. Just before it hits the ground, its speed is

• A. the square root of 2gh
• B. 2gh
• C. gh
• D. the square root of gh

Explanation: Equating the potential energy mgh to the kinetic energy half mv squared cancels the mass and gives v as the square root of 2gh, which is why all bodies fall at the same rate in the absence of air resistance. The same result follows from the equations of motion. Doubling the height increases the landing speed only by a factor of the square root of two.

19. Power is defined as

• A. the total work done
• B. the rate at which work is done or energy is transferred
• C. the force multiplied by the distance
• D. the energy stored in a body

Explanation: One watt is one joule per second, so power tells you how quickly energy is delivered rather than how much. Two motors may do the same work while one takes half the time and therefore has twice the power. Power can also be written as force multiplied by velocity when the force is constant.

20. A pump raises 100 kg of water through 10 m in 20 seconds. Taking g as 10 m per second squared, its power output is

• A. 500 W
• B. 1000 W
• C. 200 W
• D. 10000 W

Explanation: The work done is mgh, that is 100 multiplied by 10 multiplied by 10, giving 10,000 J, and dividing by 20 seconds gives 500 W. Forgetting to divide by the time leaves the 10,000 distractor, which is the energy rather than the power. The pump's input power would be higher than this, since no machine is fully efficient.